Question: $-10cd - 7ce - 2c + 1 = -2d - 9$ Solve for $c$.
Solution: Combine constant terms on the right. $-10cd - 7ce - 2c + {1} = -2d - {9}$ $-10cd - 7ce - 2c = -2d - {10}$ Notice that all the terms on the left-hand side of the equation have $c$ in them. $-10{c}d - 7{c}e - 2{c} = -2d - 10$ Factor out the $c$ ${c} \cdot \left( -10d - 7e - 2 \right) = -2d - 10$ Isolate the $c$ $c \cdot \left( -{10d - 7e - 2} \right) = -2d - 10$ $c = \dfrac{ -2d - 10 }{ -{10d - 7e - 2} }$ We can simplify this by multiplying the top and bottom by $-1$. $c= \dfrac{2d + 10}{10d + 7e + 2}$